Algebra: Einführung in die Galoistheorie
- ISBN-10
- 3110290715
- ISBN-13
- 9783110290714
- Series
- Algebra
- Category
- Mathematics
- Pages
- 331
- Language
- German
- Published
- 2013-08-29
- Publisher
- Walter de Gruyter
- Author
- Gernot Stroth
Description
Dieses Lehrbuchbietet eine Einführung in die grundlegenden Methoden der Galoistheorie. Am Beispiel der Auflösbarkeit von Polynomgleichungen durch Radikale wird das Zusammenwirken dreier Theorien – Gruppentheorie, Körpertheorie und Ringtheorie – zur Lösung dieses Problems demonstriert. Behandelt werden neben den üblichen Grundbegriffen wie Gruppen, Körper und Ringe sowie den Resultaten der Galoistheorie auch Anwendungen auf Konstruktionen mit Zirkel und Lineal, endliche Körper und Kreisteilungskörper sowieAuflösungsformeln der Gleichungen vom Grad höchstens 4. Darüber hinaus wird der konkreten Berechenbarkeit und den Algorithmen zur Bestimmung irreduzibler Teiler von Polynomen bzw. der Galoisgruppe eines moderaten Polynoms ein breiter Raum gewidmet. Die vorliegende zweite Auflage enthält Erweiterungen zu den Themen rein inseparable Körpererweiterungen, p-adische Zahlen und Bewertungstheorie, angeordnete Körper undSatz von Sturm.
Get the book
Other editions
-
- 2011-05-02
- 433 pages
- Ebook
- Walter de Gruyter
-
- 2000
- 410 pages
- Paperback
- Walter de Gruyter
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